$\dfrac{ -7a + 8b }{ 2 } = \dfrac{ -a + 4c }{ -5 }$ Solve for $a$.
Answer: Multiply both sides by the left denominator. $\dfrac{ -7a + 8b }{ {2} } = \dfrac{ -a + 4c }{ -5 }$ ${2} \cdot \dfrac{ -7a + 8b }{ {2} } = {2} \cdot \dfrac{ -a + 4c }{ -5 }$ $-7a + 8b = {2} \cdot \dfrac { -a + 4c }{ -5 }$ Multiply both sides by the right denominator. $-7a + 8b = 2 \cdot \dfrac{ -a + 4c }{ -{5} }$ $-{5} \cdot \left( -7a + 8b \right) = -{5} \cdot 2 \cdot \dfrac{ -a + 4c }{ -{5} }$ $-{5} \cdot \left( -7a + 8b \right) = 2 \cdot \left( -a + 4c \right)$ Distribute both sides $-{5} \cdot \left( -7a + 8b \right) = {2} \cdot \left( -a + 4c \right)$ ${35}a - {40}b = -{2}a + {8}c$ Combine $a$ terms on the left. ${35a} - 40b = -{2a} + 8c$ ${37a} - 40b = 8c$ Move the $b$ term to the right. $37a - {40b} = 8c$ $37a = 8c + {40b}$ Isolate $a$ by dividing both sides by its coefficient. ${37}a = 8c + 40b$ $a = \dfrac{ 8c + 40b }{ {37} }$